Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D373 | C2 | semidirect |
| 3. #26045791 | C2 | semidirect |
| 4. #26045778 | C2 | semidirect |
| 5. #26045777 | C2 | semidirect |
| 6. #26045774 | C2 | semidirect |
| 7. #26045772 | C2 | semidirect |
| 8. #26045771 | C2 | semidirect |
| 9. #26045768 | C2 | semidirect |
| 10. #26045750 | C2 | semidirect |
| 11. C22⋊Q8×C373 | C2 | semidirect |
| 83. C373 | #536 | semidirect |
| 94. C22⋊Q8 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238610 | 2 |
| C2×Q8×D373 | 2 |
| #26045791 | 2 |
| #26045778 | 2 |
| #26045777 | 2 |
| #26045774 | 2 |
| #26045772 | 2 |
| #26045771 | 2 |
| #26045768 | 2 |
| #26045750 | 2 |
| C22⋊Q8×C373 | 2 |
| #536 | 373 |